Heat water and sugar in a small saucepan over medium heat until sugar dissolves. Cool. Pour sugar syrup into a large bowl. Stir in lime juice.
Puree strawberries in a food processor. Strain and discard seeds. Stir strawberry puree and rum into syrup mixture. Pour into 13 x 9-inch metal baking pan.
Freeze for 3 hours, stirring every hour.
To serve, place mixture in food processor and pulse for 5 seconds to make a snowlike mixture. Spoon into serving dishes and serve immediately, garnished with additional strawberries, lime and mint, if desired. Makes 6 servings.
